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University of Nebraska -- Lincoln
Lincoln, Nebraska 68588
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Date | Subject | Homework |
1/8 | Functions of two variables (12.1) | 12.1:1, 2, 5, 11, 23, 25, 29, 30 |
1/9 | Contours, level curves and isoclines (parts of 12.2-4) | 12.2: 11, 13, 14, 17 (use cross sections!); 12.3: 5, 7, 8, 9. 13. 16. 20, 21ab (in your notes, we drew a contour diagram for f(x,y)=x^2+y^2 on Tuesday) |
1/11 | Linear functions, contours and cross sections for graphing (parts of 12.2-4) | 12.2: 1, 2, 15, 17 (for these, draw contours/cross sections!); 12.4: 1-5, 7, 8, 10, 13, 21, 28; Draw cross sections for f(x,y) = (x^{2} + y^{2})^{1/2} and determine what surface it is |
1/14 | Graphing surfaces and a surface zoo (parts of 12.2, 12.5) | 12.2: 4, 5, 8, 10, 16; For each surface on page 671, use the given equation (choosing non-zero values for a,b,c,d) to draw contours and x- and y-cross-sections. Describe these in words, then draw a graph of the surface using your work. |
1/15 | Functions of 3 variables (12.5) | 12.5: 1-3, 8-11, 15, 16-18, 23, 31 |
1/16 | Limits in higher dimensions (12.6) | 12.6: 1, 3, 6, 11, 13, 18 |
1/18 | Vectors (13.1, 13.2) | 13.1: 1, 5, 7, 12, 15, 28, 29, 31, 40; 13.2: 1-5, 7, 11, 21, 25 |
1/22 | The dot product (13.3) | 13.3: 1, 5, 7, 9, 11, 15, 17, 19, 33, 39, 41, 43, 49 |
1/23 | The cross product (13.4) | 13.4: 2, 3, 9, 11-13, 19, 21, 27 |
1/25 | First look at partial derivatives (14.1) | 14.1: 1, 3, 5, 9-11, 16, 17, 20, 22, 25 (Hint on these: just use what you know about normal derivatives! Also, check the section for alternate notation I didn't get to in class.) For Wednesday's review: construct an outline of everything we have done so far in the class -- be sure to indicate particular techniques and their applications. |
1/28 | Computing partial derivatives and the tangent plane (14.2-3) | 14.2: 1, 3-5, 9, 11, 18, 23, 26, 27, 36, 43 14.3: 1, 2, 5, 6, 9, 11, 18, 20, 22, 29 |
1/29 | Directional derivatives and the gradient vector (14.4) | 14.4: 1, 4, 5, 7, 15, 17, 22, 24, 27, 29-31, 33 |
1/30 | Exam 1 review -- bring your outlines and questions! | |
2/1 | Exam 1: 12.1-6, 13.1-4, 14.1-4 | |
2/4 | The gradient vector in three dimensions (14.5) | 14.4:37, 41, 47, 49-50, 53-55, 59, 65, 68-69 14.5: 2, 3, 7, 9, 14, 17, 25, 26, 49, 53 |
2/5 | Chain rules (14.6) | 14.6:21-21-24, 28, 29 |
2/6 | Chain rule applications (14.6) | 14.6: 1, 2, 3, 7, 12, 15-18, 25, 31 |
2/8 | Second partials (14.7) | 14.7: 1, 3, 6, 11, 13, 14, 19, 23, 25, 30, 33, 35, 44 |
2/11 | Critical Points (15.1) | 15.1: 1-3, 6, 7, 9, 11, 21, 22, 26 For problems 3 and 6, plug in nearby points or reason about the function to get the answer. For problems 7, 9, 11 and 26, just find the critical points -- you will classify them tomorrow. |
2/12 | Classifying Critical Points (15.1) | 15.1: 6, 7, 9, 11, 17, 22, 26, 32 |
2/13 | Global Extrema (15.2) | 15.2: 2, 7, 18, 20, 23 |
2/15 | Lagrange Multipliers (15.3) | 15.3: 1, 11, 13, 18, 19, 22, 43 |
2/18 | Double Integrals (16.1) | 16.1: 1,9,11,13,19,26,30 |
2/19 | Iterated Integrals (16.2) | 16.2: 1-4, 9, 11, 13, 17, 21, 27, 31, 33, 34, 37, 44 |
2/20 | Triple Integrals (16.3) | 16.3: 5, 7, 13, 15, 25, 26, 27, 32, 49, 51, 56, 57 |
2/22 | Integration in Polar Coordinates (16.4) | 16.4: 10, 11, 12, 16, 20, 21, 23, 24, 26, 28 |
2/25 | Review for exam 2 | |
2/26 | Cylindrical and Spherical Coordinates (16.5) | 16.5: 1, 2, 3, 5, 10, 14-16, 25, 26, 28 |
2/27 | Cylindrical and Spherical Coordinates continued (16.5) | 16.5: 34, 35, 40, 52, 55, 56, 57, 63 |
3/1 | Exam 2: 14.6-7, 15.1-3, 16.1-4 | |
3/4 | Parameterized Curves (17.1) | 17.1: 1, 4-7, 9, 19, 21, 22, 26, 28, 29, 35, 49, 70 |
3/5 | Velocity and Acceleration Vectors (17.2) | 17.2: 1, 3, 7, 8, 10, 17, 32, 36, 37, 41 |
3/6 | Vector Fields and Flows (17.3-4) | 17.3: 1, 2, 4, 5, 7, 9, 13, 15, 16, 20, 26, 27, 33 17.4: 1, 5, 8, 9, 17, 18, 20 |
3/11 | Line Integrals (18.1) | 18.1: 1-8, 11, 16, 18-21, 24, 26, 33, 36, 42, 46 |
3/12 | Computing Line Integrals (18.2-3) | 18.2: 1, 3, 5, 10, 11, 16, 20, 23, 29, 30, 31 |
3/13 | Path independence and the FTC (18.3-4) | 18.3: 3, 5, 6, 8, 9, 13, 18-20, 22, 23, 29, 31. 49 18.4: 1, 5, 9 |
3/15 | Green's Theorem (18.4) | 18.4: 14, 17, 21, 23, 26, 33, 34 |
3/18-22 | Spring Break | |
3/25 | Exam 3 review | |
3/26 | Parameterizing surfaces (17.5) | 17.5: 1,5,9-12, 13,17,18,23-25,30,33 |
3/27 | Flux integrals in the simplest case (19.1) | 19.1: 1,2,5,6,9,12,13 |
3/29 | Exam 3: 16.5, 17.1-4, 18.1-4 | |
4/1 | Computing flux integrals (19.1-19.2) | 19.1: 14, 15, 20, 27, 29, 36, 43-47 19.2: 1, 3, 5, 6 |
4/2 | Computing flux integrals (cont) (19.2) | 19.2: 10,14,16,18,26 |
4/3 | Flux integrals over parameterized surfaces (19.3) | 19.3: 1-9 |
4/5 | Computing flux integrals using spherical and cylindrical coordinates (19.2) | 19.2: 8,9,15,17,19,21,23 |
4/8 | Divergence (20.1) | 20.1: 1,2,6,10,16,19,20,27 |
4/9 | The divergence theorem (20.2) | 20.2: 1,2,5,7,14,16,20,29 |
4/10 | The curl of a vector field (20.3) | 20.3: 1,2,4,9,11-14 |
4/12 | Stokes' Theorem (20.4) | 20.3: 22, 29, 31, 35 20.4: 1-3, 8, 10 |
4/15 | Stokes' Theorem (cont) (20.4) | 20.4: 2-3, 10, 13,17,23,31 (yes, there are repeats -- there was a dearth of volunteers today!) |
4/16 | Fundamental theorems (20.5) | |
4/17 | Exam 4 Review | |
4/19 | Exam 4: 17.5, 19.1-19.3, 20.1-20.5 | |
4/22 | Review | |
4/23 | Review | |
4/24 | Review | |
4/26 | Review |